Tomographic imaging methods are characterized in that inner structures of an examination object can be examined without the need to perform an operation on the examination object. One possible type of tomographic image generation consists in recording a number of projections of the object to be examined from different angles. A two-dimensional sectional image or a three-dimensional volume image of the examination object can be calculated from these projections.
An example of such a tomographic imaging method is computed tomography. Methods for scanning an examination object with a CT system are generally known, with use being made here for example of circular scans, sequential circular scans with feed motion or spiral scans. Other types of scans that are not based on circular motions are also possible, e.g. scans with linear segments. Using at least one x-ray source and at least one opposing detector, absorption data of the examination object is recorded from different recording angles and the absorption data or projections collected in this way are allocated by way of corresponding reconstruction methods to sectional images through the examination object.
For reconstructing computed tomography images from x-ray CT datasets of a computed tomography device (CT device), i.e. from the captured projections, what is known as Filtered Backprojection (FBP) is nowadays used as the standard method. Following data capture a so-called “rebinning” step is normally performed, in which the data generated with the fan-shaped beam emanating from the source is reordered so that it is present in a form as if the detector was being hit by x-ray beams traveling toward it in parallel. The data is then transformed into the frequency domain. Filtering takes place in the frequency domain, and the filtered data is then transformed back. With the aid of the data resorted and filtered in this way, a backprojection onto the individual voxels within the volume of interest then takes place. However, with the traditional FBP methods problems arise with so-called low-frequency cone beam artifacts and spiral artifacts as a result of the approximative way in which they work. Furthermore, in traditional FBP methods the image definition is linked to the image noise. The higher the definition achieved, the higher also the image noise and vice versa.
Hence iterative reconstruction methods have recently been developed, with which at least some of these limitations can be eliminated. In such an iterative reconstruction method initial image data is first of all reconstructed from the projection measured data. To this end, for example, a convolution backprojection method can be used. Then from this initial image data synthetic projection data is generated with a “projector”, a projection operator, which should map the measuring system mathematically as closely as possible. The difference from the measured signals is then backprojected with the operator adjoining the projector and in this way a residual image is reconstructed, with which the initial image is updated. The updated image data can in turn be used in a next iteration step to generate new synthetic projection data with the aid of the projection operator, and from this again to form the difference from the measured signals and to calculate a new residual image, with which again the image data for the current iteration stage is improved, etc. Using such a method, image data can be reconstructed which has a relatively good image definition and nevertheless a low image noise. Examples of iterative reconstruction methods are the algebraic reconstruction technique (ART), the simultaneous algebraic reconstruction technique (SART), iterated filtered backprojection (IFBP), or even statistical iterative image reconstruction techniques.